When apply the mirror modifier when rigging a character
You'd better apply before rigging or shapekeying:

Rigging: It's always simpler to apply the Mirror modifier in my opinion, as you'll avoid bad surprises later on, even though you should be able to keep it in theory. If you keep it, as reminded here by Nathan, don't forget to put the Mirror modifier above the Armature modifier and enable its Vertex Groups option.
Shapekeys: You won't be able to apply the Mirror if you've created some shapekeys, so you'll have to recreate your shapekeys.